reserve X, Y for non empty set;

theorem
  for f,g being Membership_Func of X holds min(f,g) c= f
proof
  let f,g be Membership_Func of X;
  let x be Element of X;
  min(f,g).x = min(f.x,g.x) by FUZZY_1:def 3;
  hence min(f,g).x <= f.x by XXREAL_0:17;
end;
